ESurfEarth Surface DynamicsESurfEarth Surf. Dynam.2196-632XCopernicus PublicationsGöttingen, Germany10.5194/esurf-7-77-2019Environmental signal shredding on sandy coastlinesEnvironmental signal shredding on sandy coastlinesLazarusEli D.e.d.lazarus@soton.ac.ukhttps://orcid.org/0000-0003-2404-9661HarleyMitchell D.https://orcid.org/0000-0002-1329-7945BlenkinsoppChris E.TurnerIan L.https://orcid.org/0000-0001-9884-6917Environmental Dynamics Lab, School of Geography and Environmental Science, University of Southampton, Southampton, UKWater Research Laboratory, School of Civil and Environmental Engineering, University of New South Wales, Sydney NSW, AustraliaResearch Unit for Water, Environment and Infrastructure Resilience (WEIR), University of Bath, Bath, UKEli D. Lazarus (e.d.lazarus@soton.ac.uk)18January201971778621September20181October201820December20187January2019This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://esurf.copernicus.org/articles/7/77/2019/esurf-7-77-2019.htmlThe full text article is available as a PDF file from https://esurf.copernicus.org/articles/7/77/2019/esurf-7-77-2019.pdf
How storm events contribute to long-term shoreline change over
decades to centuries remains an open question in coastal research. Sand and
gravel coasts exhibit remarkable resilience to event-driven disturbances,
and, in settings where sea level is rising, shorelines retain almost no
detailed information about their own past positions. Here, we use a
high-frequency, multi-decadal observational record of shoreline position to
demonstrate quantitative indications of morphodynamic turbulence – “signal
shredding” – in a sandy beach system. We find that, much as in other dynamic
sedimentary systems, processes of sediment transport that affect shoreline
position at relatively short timescales may obscure or erase evidence of
external forcing. This suggests that the physical effects of annual (or
intra-annual) forcing events, including major storms, may convey less about
the dynamics of long-term shoreline change – and vice versa – than coastal
researchers might wish.
Introduction
Quantifying magnitudes and rates of shoreline change is fundamental to
understanding the dynamics of coastlines: not only how they behave over time,
but also how they may respond to future changes in environmental forcing.
From a coastal-management perspective, shoreline change may constitute a
coastal hazard – either event-driven, like the impact of a major storm, or
chronic, like persistent shoreline erosion from a net-negative sediment
budget. Long-term, continuous measurement of shoreline position observed at a
given location will record changes arising from event-driven and chronic
forcing alike. But how punctuated storm events contribute to long-term
shoreline change over decades to centuries remains an open question,
particularly in the context of shoreline-change prediction (Morton et al.,
1994; Fenster et al., 2001; Houser and Hamilton, 2009; Anderson et al., 2010;
Masselink and van Heteren, 2014; Brooks et al., 2016; Masselink et al., 2016;
Scott et al., 2016; Burvingt et al., 2017).
Evidence of coastal storm frequency and magnitude over centuries to
millennia may be stored in the sedimentary stratigraphy of beach ridges
(Tamura, 2012) and washover into back-barrier lagoons (Donnelly and
Woodruff, 2007). Ridge and washover stratigraphy offers a window into
climatic forcing conditions in the recent geologic past but is not a direct
measure of shoreline position. Indeed, in transgressive settings (in which
relative sea level is rising), the shoreline itself retains almost no
detailed information about its own past positions. Sand and gravel
coastlines, especially, reflect remarkable resilience to event-driven
disturbances – even to tsunamis (Choowong et al., 2009). Storm-driven
shoreline excursions on the order of ∼101–102 m
may be obscured within days to months, and effectively erased within years
(Birkemeir, 1979; Egense, 1989; Thom and Hall, 1991; Morton et al., 1994;
Douglas and Crowell, 2000; Honeycutt et al., 2001; Zhang et al., 2002; List
et al., 2006; Lazarus et al., 2012; Lentz et al., 2013; Coco et al., 2014;
Masselink and van Heteren, 2014; Phillips et al., 2017).
This coastal context exemplifies a unifying challenge in geomorphology:
determining how dynamic sedimentary systems – especially source-to-sink
pathways – respond to rapid external forcing. Processes of sediment
transport tend to rework upstream/upslope inputs so completely that their
downstream/downslope outputs may bear no resemblance to the original pattern
of forcing that drove them. In their essential synthesis of the problem,
Jerolmack and Paola (2010) call this phenomenon the “shredding” of
environmental signals. They offer that shredding – or, more formally,
“morphodynamic turbulence” – behaves much like fluid turbulence, in that
“energy injected at one frequency is smeared across a range of scales”.
High-frequency signals of external forcing are especially likely to be
shredded. Drawing on the physics of turbulent fluid flows (Frisch and
Kolmogorov, 1995), Jerolmack and Paola (2010) used time series of sediment
flux from physical and numerical experiments – bedload transport in a flume
channel (Singh et al., 2009), a canonical rice-pile experiment (Frette et
al., 1996), and a numerical rice-pile model – to illustrate their argument.
Beyond source-to-sink sedimentary systems (Romans et al., 2016), signal
shredding has since been extended to spatio-temporal changes in lake levels
(Williams and Pelletier, 2015) and methane release from peatlands (Ramirez
et al., 2015).
(a) Narrabeen–Collaroy beach, with locations of long
time-series profiles (circled numbers) and Argus Imaging System coverage.
Alongshore coordinates (y) are relative to the northern end, below
Narrabeen Headland. (b) Long-term time series of cross-shore
shoreline position (0.7 m contour) at Profile 4, measured approximately
monthly between 1976 and 2017. Time axis is in years since first measurement
(27 April 1976). (c) Time series of cross-shore shoreline position
at alongshore location y=1750 m (aligned with Profile 4), measured by
quad bike approximately monthly between 2005 and 2017. (d) Time
series of cross-shore shoreline position at alongshore location y=2340 m, measured daily by an Argus Imaging System between 2005 and 2016.
Boxes (dotted, solid) in panel (b) frame the temporal coverages for
the time series in panels (c) and (d).
Here, we investigate signal shredding in an altogether different
sediment-transport system: that of a sandy beach. Although previous studies
of sandy shoreline dynamics have invoked signal shredding conceptually
(Lazarus et al., 2011a, 2012; Williams et al., 2013), none have used
observations of shoreline position to demonstrate quantitative signatures of
signal shredding empirically. Following Jerolmack and Paola (2010), we find
the hallmarks of morphodynamic turbulence in time series of shoreline
position measured at Narrabeen–Collaroy Beach, in southeast Australia (Short
and Trembanis, 2004; Harley et al., 2011a, 2015; Turner et al., 2016; Phillips
et al., 2017). The potential for beaches to “shred” large-magnitude changes
in shoreline position forced at relatively short (∼
intra-annual) timescales complicates the reconciliation of short-term beach
dynamics and long-term, spatio-temporal patterns of shoreline variability
and evolution.
Setting and datasets
The Narrabeen–Collaroy embayment (Fig. 1a) holds a sandy beach 3.6 km long
and is one of only a few sites worldwide where ongoing beach monitoring has
been regular, frequent, and uninterrupted for multiple decades (Turner et
al., 2016). Cross-shore profiles at five locations along the beach (Fig. 1a)
have been measured approximately monthly (Fig. 1b) since 1976 (Turner et al.,
2016). In addition, continuous alongshore shoreline positions derived from
real-time kinematic GPS (RTK-GPS) quad-bike surveys of the full three-dimensional subaerial beach have been
recorded approximately monthly (Fig. 1c) between 2005 and 2017 (Harley and
Turner, 2008; Harley et al., 2011a, b, 2015). Daily-averaged shoreline
position in the southern half of the embayment (Fig. 1a) has also been
captured by an Argus Coastal Imaging
system (Fig. 1d) for over a decade (Phillips et al., 2017). In each of these
datasets we used the 0.7 m AHD (Australian Height Datum) elevation contour
to define the cross-shore shoreline position (x) at all positions
alongshore (y), commensurate with mean high water (Harley et al., 2011a,
b). Data gaps in the profiles and time series were filled by linear
interpolation. We also used deep-water wave data compiled from hourly records
logged between 2005 and 2017 by the Sydney waverider buoy, located
approximately 11 km offshore of the study area.
Shoreline-change analysis (upper panels): alongshore median of the
absolute value of monthly shoreline change from (a) long-term
Profiles 1, 2, 4, 6, and 8, (b) monthly shoreline position from the
RTK-GPS quad-bike surveys, and (c) a 850 m reach of the Argus
coverage (y=1950–2800 m). (d) Wavelet-derived power spectra
for the three shoreline-change signals, respectively, showing a transition
from non-stationary to stationary at timescales ∼101 months. A power
function fitted to the three spectra, combined, for scales up to ∼12 months, returns a scaling exponent =0.66. Storm-wave analysis (lower
panels): (e) monthly and (f) daily total storm wave-energy
flux between 2005 and 2017 (normalized to their respective maxima), used here
to represent forcing input. (g) Power spectra for the storm-wave
energy flux in panels (e) and (f). Labelled circles
emphasize major peaks in spectral density at various timescales. Grey bar in
panels (d) and (g) indicates an estimated characteristic
timescale Tc=4–6 months, based on normalized beach width
relative to mean normalized wave-energy forcing.
AnalysisPatterns in power spectra
In their bedload and rice-pile examples, Jerolmack and Paola (2010)
collapsed these physical systems into one dimension – a time series of
sediment flux past a single point. In our beach example, rather than
considering sediment flux directly, we tracked the change in shoreline
position, dx (in m), between consecutive time steps at a given position
alongshore (y). In a generic source-to-sink system in which sediment only
moves downstream, sediment flux is unidirectional and positive. By contrast,
in a one-dimensional treatment of a beach system, shoreline movement
(dx) is bidirectional, as wave-driven cross-shore sediment transport
shifts the shoreline at any location onshore and offshore over time. To
therefore include both onshore (negative) and offshore (positive) movement,
we worked with the absolute value of shoreline change and calculated the
power spectrum of the time series using wavelet analysis, following the
method described by Lazarus et al. (2011a, 2012). We show results based on
the median absolute value of shoreline change for all positions alongshore
at a given time step (Fig. 2a–c). To confirm that this simplification is
representative, we also analysed the spectral density of the
shoreline-change time series at each position alongshore (Fig. S1 in the Supplement).
This application of wavelet analysis functions much like a Fourier transform
(Lazarus et al., 2011a, 2012). We first convolved the time series (the
absolute value of shoreline change) with a second-order Daubechies wavelet
in a continuous wavelet transform. Taking the mean transform variance at
temporal scales up to approximately half the overall length of the signal
produced a measure of spectral power. We chose a wavelet with a small number
of vanishing moments – a measure of how much the wavelet shape undulates –
because simple wavelets tend to have better sensitivity over a greater range
of scales. The general pattern of spectral density was insensitive to
different wavelets with low vanishing moments and was comparable to spectra
generated by a fast Fourier transform (Fig. S2).
Like the sedimentary systems described by Jerolmack and Paola (2010), the
spectral density of the one-dimensional shoreline-change term dx(t)
yields a pattern with two regimes (Fig. 2d). A non-stationary regime extends
over shorter timescales, such that spectral density and timescale are
correlated by a power law. This relationship transitions at ∼9–11 months into a comparatively stationary (uncorrelated) regime over
longer intervals. (A power function fitted to the three spectra, combined,
for scales up to ∼12 months, returns a scaling exponent =0.66, but
the physical significance of this slope value remains unclear.) This
two-regime pattern in the power spectrum (Jerolmack and Paola, 2010) serves
as an initial indication that signal shredding may be inherent in the
dynamics of sandy beach systems.
But what environmental signal is being shredded at the shoreline? Consider
again a unidirectional source-to-sink system, driven by some input flux at
the upstream end. That input flux might be constant; it might fluctuate
quasi-periodically; it might spike with large-magnitude events. In a
controlled physical experiment or a numerical model, input flux (of sediment
and/or fluid) is a known quantity, set by the researcher. Whatever its
pattern in time, input flux embodies the environmental signal that is
susceptible to shredding by sediment-transport processes internal to the
system. Here, for the beach system, we treated energy flux from incident
storm waves as the external environmental signal that shoreline behaviour
may destroy or preserve.
Previous work on Narrabeen–Collaroy has demonstrated that the relationship
between wave-energy flux and shoreline change is strongest for storm waves
(Harley et al., 2009; Phillips et al., 2017). By isolating storm waves, we
do not mean to suggest that lower-energy waves do not move sediment.
However, changes in nearshore bar and beach morphology tend to emerge far
more slowly than the high-frequency variability of low-energy wave forcing
(Plant et al., 2006), and, in this case, we are interested in the conditions
under which an input flux could be preserved in the shoreline response
signal. We defined storm-wave conditions by a threshold corresponding to the
95th percentile of deep-water significant wave height (Hs, m), which for
this region is Hs>3 m (Harley, 2017). Much like flow
discharge in a fluvial system, deep-water wave-energy flux (E, kW per metre wavefront) may serve as a useful proxy for input flux to the beach:
E=ρg264πHs2Pw≈0.5Hs2Pw,
where ρ (kg m-3) is water density, g (m s-2) is
acceleration by gravity, Hs (m) is significant deep-water wave
height, and Pw (s) is wave period (Herbich, 2000).
We calculated monthly and daily total storm-wave energy fluxes corresponding
to the monthly and daily shoreline time series (Fig. 2e, f) and transformed
them into power spectra to demonstrate that the forcing (input) and response
(output) spectra are not the same (Fig. 2d, g). Where the spectral density of
shoreline change is non-stationary (correlated) over a range of relatively
short timescales (Fig. 2d), the spectral density of wave forcing is
comparatively stationary (uncorrelated) over the same range (Fig. 2g). The
monthly wave-energy time series shows a peak in spectral density at ∼24 months but with no clear comparator in the shoreline-change spectra. The
daily wave-energy spectrum rises at the long-interval end of its range to a
broad peak at ∼30–45 months (Fig. 2g), which overlaps with a local
maximum in the shoreline-change spectra at ∼37–42 months (Fig. 2d).
Even in this one-dimensional representation, the sediment-transport
processes of shoreline change have transformed an input signal into a
quantitatively distinct output signal. To place these input–output spectral
patterns in the context of physical processes that might explain them, we
explored characteristic timescales of key embayed-beach dynamics.
Characteristic timescale from system size and input flux
Jerolmack and Paola (2010) showed in their exemplars that the transition from
non-stationary to stationary (correlated to uncorrelated) in the spectral
density of the output signal occurs at an intrinsic, characteristic
timescale Tc. Theoretically, Tc is set by the system
size L relative to the constant (∼ mean) signal input. While those
parameters can be dictated for experimental systems, they are less clear for
an open sandy coastline. To independently estimate Tc in the
Narrabeen–Collaroy system and compare the results to the timescale (or range
of timescales) at which the shoreline-change power spectra transition from
non-stationary to stationary, we tested two different approaches.
The first approach is a back-of-the-envelope exercise. We assumed that the
system size L is equivalent to maximum cross-shore beach width, defined here
as the cross-shore distance from a fixed landward reference point to mean
sea level (Harley and Turner, 2008; Harley et al., 2011b). This assumption
extends from having collapsed the system into only the cross-shore (x)
dimension: at any alongshore position (y), the theoretical maximum
cross-shore (x) extent to which the beach can ever erode is the full width of
the beach L, independent of embayment length. (We call L the “theoretical
maximum” because historical records of shoreline change are necessarily of
finite duration and therefore may never reflect this full width.) We
normalized L relative to its maximum value, such that the theoretical maximum
L=1. For the input flux, we took the mean normalized monthly (and daily)
total wave-energy flux over the full span of the dataset, which here serves
the purpose for a rough estimate of Tc. Using monthly total storm-wave
energy flux (Fig. 2e), L/E (where L and E are both normalized) yields Tc=4–6 months; using the daily total storm-wave energy flux (Fig. 2f),
Tc=5–6 months. (These ranges come from excluding and including,
respectively, zero values in the total wave-energy time series, which
increases or decreases the mean normalized E.) Note that this estimate aligns
with a detailed analysis of timescales for beach recovery at
Narrabeen–Collaroy (Phillips et al., 2017). Plotted in relation to the power
spectra for shoreline change (Fig. 2d), the characteristic timescale marks
approximately where the spectral density “rolls over” from non-stationary to
stationary (correlated to uncorrelated), just ahead of the distinct local
maximum at ∼9–11 months.
Characteristic timescale from modes of embayed beach dynamics
The second approach to estimate one or more characteristic timescales Tc
for the Narrabeen–Collaroy system derives from shoreline behaviours typical
of this site and of embayed beaches more generally (Short and Trembanis,
2004; Ranasinghe et al., 2004; Harley et al., 2011a, 2015; Ratliff and
Murray, 2014).
(a) Detrended (in time) shoreline position, measured
approximately monthly by quad bike, with north at left (corresponding to
Fig. 1a). (b) Orthogonal PCA modes (or empirical orthogonal function (EOF) modes), representing variance about the mean shoreline position, and
(c) wavelet-derived power spectra of each mode, where the first
local maximum indicates the characteristic timescale for that
mode.
Although they vary in detail between specific locations, approximately four
modes of shoreline behaviour tend to describe how sediment moves within
embayed beach systems. One mode represents sediment cycling offshore and
onshore as a quasi-coherent unit at the full scale of the embayment: imagine
a narrow beach during stormier times of the year and a wide beach during
calmer intervals. Another common mode is termed “rotation” and occurs when
prevailing wave conditions or a storm event shifts a significant volume of
sediment inside the embayment alongshore to form a wider beach at one end
and a narrower beach at the other (Ranasinghe et al., 2004). Related to
rotation is what has been described as a “breathing” mode, a kind of
shoreline resonance that hinges near the centre of the beach and
characterizes changes in shoreline curvature, as sand moves between the
middle and ends of an embayment (Ratliff and Murray, 2014). An additional
mode of shoreline dynamics reflects patterns of shoreline variability
introduced by rhythmic movements of sandbars, sandwaves, mega-cusps, and
inlet processes, where applicable (Harley et al., 2011a, 2015). These four
modes are not necessarily hierarchical: their relative dominance can change
as a function of wave conditions (Harley et al., 2011a, 2015). More
importantly, these modes of shoreline behaviour likely manifest intrinsic
timescales.
To find characteristic timescales corresponding to the modes of shoreline
behaviour at Narrabeen–Collaroy, we followed steps described by Ratliff and
Murray (2014). From the monthly shorelines derived from RTK-GPS quad-bike
surveys, at each position alongshore we detrended the series of shoreline
position (not shoreline-position change) in time (Fig. 3a). To calculate the
empirical orthogonal modes in the alongshore dimension through time and thus
characterize shoreline variation around its mean position (Fig. 3b), we
applied principal-component analysis (PCA) (Winant et al., 1975; Aubrey, 1979; Clarke and Eliot, 1982; Hsu et al., 1994;
Dail et al., 2000; Short and Trembanis, 2004). Each mode in sequence explains
a smaller percentage of variation in the data. We then used a continuous
wavelet transform, again finding the mean transform variance over a range of
time intervals (Lazarus et al., 2011a), to examine the spectral signatures of
the first four behavioural modes in the temporal dimension. In the resulting
power spectrum, peaks represent the characteristic timescale for each
behavioural mode (Ratliff and Murray, 2014). We take Tc (Fig. 3c)
as the first local maximum in the power spectrum (Ratliff and Murray, 2014),
using a Ricker–Marr wavelet. (Other Gaussian-type wavelets yielded similar
power spectra and characteristic timescales.)
The first two modes in these data are both rotational (Fig. 3b). The first, a
rotation toward the north, accounts for 51 % of the observed shoreline
variability with a peak timescale at ∼21 months (and a local saddle at
∼12 months). The second, a rotation toward the south, accounts for
32 % (∼6–7 months) and agrees closely with the Tc
calculated independently from the normalized storm wave-energy flux. In
previous applications of PCA to >25 years of long-term profile data (Short and
Trembanis, 2004) and 5 years of quad-bike measurements (Harley et al., 2011a,
2015) at Narrabeen–Collaroy, rotational behaviour was secondary (26 % of
shoreline variability around its mean position) to a dominant mode (∼60 %) of quasi-coherent, off- and onshore sand movement within the
embayment. In the extended quad-bike dataset used here (Fig. 3a),
bi-directional rotation appears to become the predominant mode after ∼2010. The third and fourth modes account for 5.4 % (∼10–11 months) and 2.5 % (∼10–11 months) of observed shoreline
variability, respectively, and might reflect breathing behaviour at the
fulcrum and both ends of the beach, perhaps with influences from other
sources of shoreline variability, including an ephemeral inlet near Narrabeen
Headland (Fig. 1a). Approach angles of deep-water waves associated with
different types of storm system likely control the occurrence and relative
strengths of the various modes (Harley et al., 2011a, 2015).
Although resolved in two dimensions, these shoreline behaviours nevertheless
inform our one-dimensional simplification of shoreline change (Fig. 2). The
spatial analysis shows that at each position alongshore, shoreline position
is moving onshore and offshore with a few dominant modes of
sediment-transport dynamics that rework the embayed beach at characteristic
timescales. The “closed” system of the embayment makes the beach behave as
a roughly conserved physical quantity. This means that rotation-driven
shoreline change is spatially correlated, such that one side accretes
approximately as much as the other side erodes. The spectral density of
shoreline change over time at any position (y) is insensitive to this spatial
correlation because the absolute value of shoreline change makes the
magnitudes at one end of the embayment approximately equal to those at the
other, and thus their power spectra quantitatively similar, in turn.
Discussion and implications
Jerolmack and Paola (2010) showed that morphodynamic turbulence will tend to
shred (strongly modify) input perturbations with timescales shorter than
the characteristic timescale of the system (T<Tc). Only input
perturbations with timescales T>Tc are likely to be preserved (or only
weakly modified) in the output signal. The various characteristic
timescales that we estimated for the Narrabeen–Collaroy system (Fig. 4;
Table 1) suggest that input perturbations (i.e. wave-energy events) with
timescales on the order of T<∼101 months are subject to
distortion by morphodynamic turbulence, and their effects on shoreline
change will tend to get “smeared” across a range of temporal scales in the
output signal (Fig. 4).
By extension, irregular but multi-annual forcings, such as the El
Niño–Southern Oscillation (ENSO), might have a timescale sufficiently
long enough to avoid erasure by annual cycling (Barnard et al., 2015). The
power spectra for the shoreline-change and daily-resolution storm-wave
energy flux register a peak near a time interval of ∼3–4 years, consistent with ENSO forcing. Moreover, if climate-related drivers
were to increase future forcing at the annual timescale (T≈Tc),
perhaps through storm frequency or intensity or both (Emanuel, 2013), there
is potential for system resonance (Binder et al., 1995; Cadot et al., 2003;
Jerolmack and Paola, 2010) that could amplify corresponding shoreline
changes.
Compilation of power spectra from shoreline-change data in relation
to different characteristic timescales for environmental forcing (blue/dark
bars) and intrinsic physical processes (red/light bars). Thick black lines
indicate power spectra shown in Fig. 2d, derived from the alongshore median
absolute value of shoreline change through time (“method 1”). Thin grey
lines show the median spectral densities of power spectra of shoreline change
through time (detrended, absolute value) at each position alongshore for the
three survey types (“method 2”), shown in Fig. S1. We plot them together
here to demonstrate their comparability. Double-ended arrow indicates
transition zone in the spectral density from non-stationary to stationary by
a temporal interval on the order of ∼101 months.
Compilation of characteristic timescales in Figs. 2 and 4.
Data sourceCharacteristictimescales (months)Shoreline-change datasets Method 1 (alongshore median absolute value of shoreline change) Long-term profiles (monthly)11, 37–42Quad-bike surveys (monthly)11, 37–42Argus system (daily)∼1, 9, 23Method 2 (median spectral power of absolute value of shoreline change over time at each position alongshore) Long-term profiles (monthly)11–12, 42, 56Quad-bike surveys (monthly)12, 37–42Argus system (daily)∼1, 8–10, 26, 34Storm-wave energy forcing Estimated Tc (normalized L/E)4–6Storm-wave E flux (monthly)24Storm-wave E flux (daily)∼2, 30–45EOF modes of embayed beach behaviour Mode 1 (51 %, rotational)12–14, 21Mode 2 (32 %, rotational)6–7, 22–26Mode 3 (5.4 %, breathing and other)10–11, 36–42Mode 4 (2.5 %, breathing and other)10–11, 36–42
However, the collective effect of these various and variable characteristic
timescales is to make storm-driven perturbations difficult to isolate in
sparsely sampled records of shoreline change. If cross-shore beach recovery
is rapid – that is, if most of the sediment shifted off a beach during a
storm is stored in a nearshore bar and then swept back onshore in a matter
of days to weeks afterward (Birkemeier, 1979; List et al., 2006; Phillips et
al., 2017), then the magnitude of shoreline change driven by a storm event
may appear damped even in a monthly survey of beach position. When such
large fluctuations are so ephemeral, only high-frequency sampling can hope
to capture their fullest extents (Splinter et al., 2013; Phillips et al.,
2017). And even then, nearshore beach dynamics may still ultimately obscure
the magnitude of direct environmental forcing because of the complex
transformation that offshore wave energy undergoes across the surf zone
(Plant et al., 2006; Coco et al., 2014).
Intrinsic timescales for behavioural modes of beach change along open
coastlines may be different from those for embayed settings. Where
alongshore spatial scales are large (∼101–102 km),
the cumulative, diffusive effect of alongshore sediment transport is an
especially effective shredder (Lazarus et al., 2011a, 2012). Ratliff and
Murray (2014) suggest that the diffusive scaling evident in their modelling
results implies that characteristic timescales increase nonlinearly with
embayment length alongshore. They list other factors that could likewise
change the characteristic timescales, such as wave height, sediment type,
and the aspect ratio of headlands relative to the bay (which would affect
local wave height through wave shadowing). Broadly posed, where the
influence of alongshore sediment transport is significant and the beach
system is “open” (rather than “closed” by headlands that make sand a
conserved quantity), then the longer the beach, the more effective the
system will be at shredding high-frequency signals. Were the same
high-resolution spatio-temporal data available for ∼104 m of open sandy coastline as they are for Narrabeen–Collaroy, a comparable
analysis might highlight a series of progressively larger characteristic
timescales for reversing erosion hotspots, alongshore sand waves, and
fluctuations in alongshore curvature (List et al., 2006; Lazarus and Murray,
2007, 2011; Lazarus et al., 2011a, 2012). Signal shredding may be strongest
when coupled to human manipulations of natural shoreline behaviour (McNamara
and Werner, 2008a, b; Williams et al., 2013; Lazarus et al., 2011b, 2016).
In an ideal source-to-sink sedimentary system with perfect storage, output
flux would be faithfully recorded in the sink stratigraphy. The majority of
work in morphodynamic turbulence and signal shredding comes from efforts to
puzzle out what information stratigraphic records do and do not convey about
environmental forcing (Paola et al., 2018). For beach systems, that may mean
large forcing events like major coastal storms, even when we can record
their effects, probably tell us less about the dynamics of long-term
shoreline change – and vice versa – than we would wish to know. Empirical
evidence of signal shredding in the shoreline-position data from the
Narrabeen–Collaroy system demonstrates how, and suggests why, signatures of
individual storm impacts can be obscured or erased in long-term
observational records, even those recorded at a reasonably high temporal
resolution. Jerolmack and Paola (2010) recommend using controlled
experiments to gain vital mechanistic insight into morphodynamic turbulence.
Here, the effects of system size, input flux, the magnitudes of major
disturbance events and potential resonant amplification (T≈Tc)
could be tested systematically across a broad parameter space for coastal
systems. In exploring the dynamics of signal shredding, controlled
experiments would also illuminate characteristic timescales for fundamental
processes of sediment transport in coastal environments.
See Turner et al. (2016) for a detailed description of
datasets for the Narrabeen–Collaroy system. Data are available at
http://narrabeen.wrl.unsw.edu.au/download/narrabeen/ (UNSW Australia
Water Research Laboratory, 2019).
The supplement related to this article is available online at: https://doi.org/10.5194/esurf-7-77-2019-supplement.
EDL conceived the idea and conducted the analysis. MDH and
ILT provided processed data. All authors (EDL, MDH, CEB, and ILT) contributed
to the data interpretation and to writing the
manuscript.
The authors declare that they have no conflict of
interest.
Acknowledgements
Eli D. Lazarus thanks Andrew Ashton and Dylan McNamara for discussions about signal shredding
in shoreline data, dating back to the publication of Jerolmack and Paola (2010). This work was supported by funding (to Eli D. Lazarus) from the NERC BLUEcoast
project (NE/N015665/2) and a University of Southampton Global Partnerships
Award. Since 2004, the ongoing beach monitoring program at
Narrabeen–Collaroy has been funded by the Australian Research Council
(Discovery and Linkage), Warringah and Northern Beaches Councils, the NSW Office
of Environment and Heritage (OEH), the SIMS foundation, and the UNSW Faculty of
Engineering (see Turner et al., 2016). We are grateful to Katherine Ratliff, Andrew Ashton, and an anonymous reviewer for constructive comments that improved
the paper.
Edited by: Sebastien Castelltort
Reviewed by: Katherine Ratliff and one anonymous referee
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